@tregg76 ...
Full disclosure, the information I will share here is just what I remember from well over a year ago when I worked at a technical college in Wisconsin. I'm not sure if any processes have changed since then. Also, I was a Canvas admin there, but I did not work directly with sending data over from our SIS (Student Information System) which was Banner to Canvas, so I don't know all the details into how that all worked. Here is what I recall, though.
First, I believe there was a way that our students were emailed after they were enrolled in one or more Canvas courses. I am not sure what that email looked like, though.
Second, I know there were at least two (if not three) daily files that were sent from our SIS to Canvas. One file was the file that created the user accounts in Canvas. Another file created the Canvas course shells. The third file was the one that enrolled users into those courses. So, your process of having to go into each course and add students via SIS ID sounds time consuming to me...and not really necessary?
I'm not sure what SIS your school uses, and I wouldn't be of much help in that realm, unfortunately. Hopefully my response will be of some help in one way or another, though. I'm hopeful that someone else will be able to chime in that could be of more help.